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# If |x+1/2|=|y+1/2|, what is the value of x+y?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8005
GMAT 1: 760 Q51 V42
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If |x+1/2|=|y+1/2|, what is the value of x+y?  [#permalink]

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20 Mar 2018, 01:45
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Difficulty:

55% (hard)

Question Stats:

55% (01:37) correct 45% (01:56) wrong based on 66 sessions

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[GMAT math practice question]

If $$|x+\frac{1}{2}|=|y+\frac{1}{2}|$$, what is the value of $$x+y$$?

1) $$xy<0$$
2) $$x>0$$ and $$y<0$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7958 Re: If |x+1/2|=|y+1/2|, what is the value of x+y? [#permalink] ### Show Tags 20 Mar 2018, 02:55 MathRevolution wrote: [GMAT math practice question] If $$|x+\frac{1}{2}|=|y+\frac{1}{2}|$$, what is the value of $$x+y$$? 1) $$xy<0$$ 2) $$x>0$$ and $$y<0$$ $$|x+\frac{1}{2}|=|y+\frac{1}{2}|$$ Two cases possible.. 1) x and y are of SAME sign x=y.. Then x and y can take any value.. and thus x+y could be anything.. 2) x and y are of different sign... x+1/2 = -y-1/2......x+y=-1 So we can get a value of x+y if they both are of OPPOSITE sign.. Let's see what each statement tells us.. (I) xy<0 X and y are of OPPOSITE sign.. Hence x+y=-1 Sufficient (II) x>0 and y<0.. So both are OPPOSITE sign.. Suff D _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8005 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If |x+1/2|=|y+1/2|, what is the value of x+y? [#permalink] ### Show Tags 22 Mar 2018, 00:50 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. $$|x+\frac{1}{2}|=|y+\frac{1}{2}|$$ $$=> |x+\frac{1}{2}|^2=|y+\frac{1}{2}|^2$$ $$=> (x+\frac{1}{2})^2=(y+\frac{1}{2})^2$$ $$=> x^2 + x + \frac{1}{4} = y^2 + y + \frac{1}{4}$$ $$=> x^2 - y^2 + x - y = 0$$ $$=> (x-y)(x+y)+(x-y) = 0$$ $$=> (x-y)(x+y+1) = 0$$ $$=> x=y or x+y=-1$$ Condition 1) Since $$xy < 0$$, we have $$x≠y$$ and $$x+y = -1$$ from the original condition. Condition 2) Since $$x > 0$$ and $$y < 0$$, we have $$x≠y$$ and$$x+y = -1$$from the original condition. Therefore, D is the answer. By Tip 1), D is most likely to be the answer. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If |x+1/2|=|y+1/2|, what is the value of x+y?   [#permalink] 22 Mar 2018, 00:50
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